Putting the R in phaRmacy
04/12/2020
All sites and drugs
Drug A
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001002 |
| ETS(quantity ~ season(method = “N”)) | l | 162.3565708 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 17.63355 | 0.0614688 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 0.6160404 | 0.1679878 | 3.667174 | 0.0002858 |
| ARIMA(quantity) | ma1 | -0.6055922 | 0.1698636 | -3.565169 | 0.0004173 |
| ARIMA(quantity) | ma2 | 0.1340922 | 0.0598298 | 2.241227 | 0.0256759 |
| ARIMA(quantity) | sar1 | 0.0981877 | 0.0639542 | 1.535283 | 0.1256726 |
| ARIMA(quantity) | constant | 56.3162905 | 3.3440977 | 16.840504 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 6.277749 | 0.7914132 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -17.955 | 99.947 | 88.679 | -Inf | Inf | 0.71325 |
| ETS(quantity ~ season(method = “N”)) | Test | -10.876 | 104.840 | 91.000 | -Inf | Inf | 0.73192 |
| prophet(quantity) | Test | 10.452 | 105.970 | 102.290 | -Inf | Inf | 0.82271 |
| SNAIVE(quantity) | Test | -92.667 | 122.390 | 104.330 | -Inf | Inf | 0.83916 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -1.0351 | 54.794 | 36.070 | -Inf | Inf | 1.05120 |
| ETS(quantity ~ season(method = “N”)) | Test | -1.6049 | 56.040 | 37.181 | -Inf | Inf | 1.08360 |
| prophet(quantity) | Test | -1.2504 | 55.974 | 35.661 | NaN | Inf | 1.03930 |
| SNAIVE(quantity) | Test | -2.3333 | 57.196 | 25.667 | -Inf | Inf | 0.74802 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -25.20535 | 117.9132 | 100.31953 | -Inf | Inf | 0.8167953 | -0.0704047 |
| ETS(quantity ~ season(method = “N”)) | Test | -24.24783 | 117.2160 | 98.46498 | -Inf | Inf | 0.8016957 | -0.1404514 |
| prophet(quantity) | Test | -15.77041 | 513.4691 | 232.46738 | -Inf | Inf | 1.8927348 | 0.0637362 |
| SNAIVE(quantity) | Test | -10.51852 | 162.4074 | 131.40741 | -Inf | Inf | 1.0699108 | -0.0374186 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 25.2303109 | 95.69321 | 56.43252 | NaN | Inf | 1.6350261 | 0.1158871 |
| ETS(quantity ~ season(“N”)) | Test | -3.7595861 | 50.47848 | 37.66326 | -Inf | Inf | 1.0912222 | -0.2326012 |
| prophet(quantity) | Test | -0.7656823 | 44.15451 | 27.73432 | NaN | Inf | 0.8035496 | 0.0899582 |
| SNAIVE(quantity) | Test | -10.6666667 | 86.64102 | 50.00000 | -Inf | Inf | 1.4486559 | -0.1252455 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001 |
| ETS(quantity ~ season(method = “N”)) | l | 2018.9770 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 271.4111 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -1.5644956 | 0.0443110 | -35.307164 | 0.0000000 |
| ARIMA(quantity) | ma2 | 0.5815256 | 0.0442398 | 13.144845 | 0.0000000 |
| ARIMA(quantity) | sma1 | 0.1117924 | 0.0564947 | 1.978812 | 0.0486708 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 56.09459 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -269.200 | 1095.30 | 815.82 | -74.093 | 93.163 | 1.3412 |
| ETS(quantity ~ season(method = “N”)) | Test | -237.780 | 908.66 | 722.17 | -61.588 | 78.739 | 1.1873 |
| prophet(quantity) | Test | -207.760 | 918.26 | 722.93 | -61.027 | 80.057 | 1.1885 |
| SNAIVE(quantity) | Test | 10.833 | 1837.60 | 1650.20 | -83.329 | 150.260 | 2.7130 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -36.0820 | 434.43 | 347.90 | -Inf | Inf | 0.96973 |
| ETS(quantity ~ season(method = “N”)) | Test | -19.4260 | 450.48 | 350.16 | -Inf | Inf | 0.97604 |
| prophet(quantity) | Test | -4.2805 | 474.53 | 323.75 | NaN | Inf | 0.90242 |
| SNAIVE(quantity) | Test | 185.2100 | 479.98 | 262.02 | -Inf | Inf | 0.73037 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 16.89737 | 671.6956 | 478.1925 | -12.580915 | 34.97243 | 0.7984274 | -0.1803572 |
| ETS(quantity ~ season(method = “N”)) | Test | -383.01074 | 668.8489 | 561.4917 | -38.504087 | 45.00228 | 0.9375103 | -0.4464899 |
| prophet(quantity) | Test | -886.02419 | 1829.0925 | 1099.5580 | -67.867259 | 75.88472 | 1.8359077 | 0.4161076 |
| SNAIVE(quantity) | Test | 65.74074 | 631.5291 | 483.0741 | -5.520615 | 33.15133 | 0.8065781 | -0.2562749 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 284.57494 | 1896.9388 | 854.1100 | NaN | Inf | 2.378887 | -0.0003884 |
| ETS(quantity ~ season(“N”)) | Test | -24.80003 | 573.8836 | 382.8588 | -Inf | Inf | 1.066347 | 0.0261571 |
| prophet(quantity) | Test | 299.79875 | 1474.7287 | 601.7404 | NaN | Inf | 1.675981 | 0.0353826 |
| SNAIVE(quantity) | Test | 98.41667 | 778.5898 | 411.0833 | -Inf | Inf | 1.144959 | 0.0780889 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001 |
| ETS(quantity ~ season(method = “N”)) | l | 3297.9622 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 159.7713 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -1.5802277 | 0.0421181 | -37.519010 | 0 |
| ARIMA(quantity) | ma2 | 0.6097934 | 0.0439426 | 13.877053 | 0 |
| ARIMA(quantity) | sma1 | 0.3502639 | 0.0583689 | 6.000861 | 0 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 64.2106 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -160.180 | 1592.4 | 1351.3 | -40.251 | 63.339 | 1.6235 |
| ETS(quantity ~ season(method = “N”)) | Test | 14.938 | 1447.0 | 1225.5 | -29.304 | 53.342 | 1.4723 |
| prophet(quantity) | Test | 121.120 | 1442.7 | 1221.5 | -23.718 | 49.736 | 1.4676 |
| SNAIVE(quantity) | Test | 10.667 | 2195.8 | 1868.0 | -48.360 | 90.024 | 2.2443 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -21.0540 | 707.47 | 528.15 | -Inf | Inf | 1.24260 |
| ETS(quantity ~ season(method = “N”)) | Test | -6.6455 | 698.07 | 514.96 | -Inf | Inf | 1.21150 |
| prophet(quantity) | Test | 11.2070 | 639.48 | 425.19 | NaN | Inf | 1.00030 |
| SNAIVE(quantity) | Test | 303.1900 | 724.97 | 387.52 | -40.53 | 142.2 | 0.91172 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -149.63190 | 955.9126 | 827.3318 | -21.87522 | 37.91886 | 1.005802 | -0.5012751 |
| ETS(quantity ~ season(method = “N”)) | Test | -206.02724 | 1229.1067 | 1055.5196 | -34.19600 | 52.75269 | 1.283213 | -0.5622976 |
| prophet(quantity) | Test | -21.45090 | 4593.8719 | 2344.8879 | -27.10815 | 105.37410 | 2.850721 | -0.0557857 |
| SNAIVE(quantity) | Test | -98.14815 | 1323.9697 | 1064.3704 | -24.69294 | 47.69068 | 1.293973 | -0.3847595 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -56.61774 | 434.3618 | 362.5953 | -Inf | Inf | 0.8628774 | 0.0660133 |
| ETS(quantity ~ season(“N”)) | Test | -123.63958 | 372.2577 | 328.5389 | -Inf | Inf | 0.7818323 | -0.3049381 |
| prophet(quantity) | Test | 11.84012 | 383.6259 | 263.0213 | NaN | Inf | 0.6259185 | 0.2713956 |
| SNAIVE(quantity) | Test | -107.25000 | 596.0340 | 382.5833 | -Inf | Inf | 0.9104433 | 0.0447512 |
Drug B
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.139557 |
| ETS(quantity ~ season(method = “N”)) | l | 59.925456 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 20.98792 | 0.021178 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 0.1505062 | 0.0881543 | 1.707304 | 0.0896019 |
| ARIMA(quantity) | ma1 | -0.8930176 | 0.0399560 | -22.350011 | 0.0000000 |
| ARIMA(quantity) | sma1 | -0.1339187 | 0.0840958 | -1.592453 | 0.1131516 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 17.7895 | 0.05862 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 87.756 | 110.140 | 87.756 | 40.53900 | 40.539 | 1.14070 |
| ETS(quantity ~ season(method = “N”)) | Test | 19.851 | 68.637 | 52.716 | 0.78951 | 24.988 | 0.68522 |
| prophet(quantity) | Test | 80.355 | 100.680 | 80.355 | 37.39700 | 37.397 | 1.04450 |
| SNAIVE(quantity) | Test | 118.830 | 136.360 | 118.830 | 59.71900 | 59.719 | 1.54460 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 11.7560 | 38.837 | 26.066 | -Inf | Inf | 1.6681 |
| ETS(quantity ~ season(method = “N”)) | Test | 7.9533 | 37.947 | 26.247 | -Inf | Inf | 1.6797 |
| prophet(quantity) | Test | 11.0910 | 35.042 | 21.390 | -Inf | Inf | 1.3688 |
| SNAIVE(quantity) | Test | 12.7620 | 36.109 | 21.238 | -Inf | Inf | 1.3591 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -13.22444 | 55.25793 | 46.09315 | -122.218255 | 142.26525 | 0.6141584 | 0.1542215 |
| ETS(quantity ~ season(method = “N”)) | Test | -16.76031 | 58.00306 | 47.60042 | -132.908220 | 150.93329 | 0.6342417 | 0.0649896 |
| prophet(quantity) | Test | -75.29404 | 246.32037 | 131.09194 | -396.326206 | 454.67008 | 1.7467066 | -0.1221946 |
| SNAIVE(quantity) | Test | 28.90909 | 68.73136 | 48.90909 | -2.714454 | 61.21138 | 0.6516787 | -0.0892070 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -16.298387 | 21.67009 | 16.29839 | -Inf | Inf | 1.0743482 | 0.0319153 |
| ETS(quantity ~ season(“N”)) | Test | -5.537031 | 12.71952 | 12.20404 | -Inf | Inf | 0.8044592 | 0.0265180 |
| prophet(quantity) | Test | -18.930928 | 30.64683 | 19.22381 | NaN | Inf | 1.2671848 | -0.1023979 |
| SNAIVE(quantity) | Test | -9.500000 | 25.28834 | 18.83333 | -Inf | Inf | 1.2414454 | -0.4487179 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.1100328 |
| ETS(quantity ~ season(method = “N”)) | l | 156.2431110 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 46.14766 | 1.3e-06 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -1.0477872 | 0.0696255 | -15.048902 | 0.0000000 |
| ARIMA(quantity) | ma2 | 0.2344245 | 0.0744485 | 3.148816 | 0.0019296 |
| ARIMA(quantity) | sma1 | 0.2730468 | 0.0902235 | 3.026339 | 0.0028512 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 13.49332 | 0.1973817 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 69.035 | 100.660 | 74.455 | 26.3140 | 62.444 | 0.69958 |
| ETS(quantity ~ season(method = “N”)) | Test | 57.970 | 95.708 | 72.598 | -9.4382 | 88.077 | 0.68213 |
| prophet(quantity) | Test | -11.603 | 76.511 | 70.608 | -128.8600 | 155.570 | 0.66343 |
| SNAIVE(quantity) | Test | -49.000 | 82.704 | 71.333 | -161.1200 | 170.090 | 0.67025 |
Daily data
## Warning in sqrt(diag(best$var.coef)): NaNs produced
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 4.16800 | 27.855 | 17.880 | -Inf | Inf | 0.59479 |
| ETS(quantity ~ season(method = “N”)) | Test | 15.12300 | 31.340 | 15.795 | NaN | Inf | 0.52542 |
| prophet(quantity) | Test | 5.22030 | 27.171 | 21.438 | NaN | Inf | 0.71315 |
| SNAIVE(quantity) | Test | -0.80952 | 36.635 | 22.810 | -Inf | Inf | 0.75878 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 27.991157 | 122.3278 | 106.09330 | -110.8304 | 156.4304 | 1.0040912 | 0.1565226 |
| ETS(quantity ~ season(method = “N”)) | Test | 26.952283 | 101.9112 | 85.27137 | -152.5941 | 188.9552 | 0.8070277 | 0.4519125 |
| prophet(quantity) | Test | 3.013169 | 129.0651 | 108.70019 | -221.6250 | 258.5854 | 1.0287634 | 0.1741823 |
| SNAIVE(quantity) | Test | -43.083333 | 133.4881 | 126.75000 | -380.0090 | 404.2968 | 1.1995910 | 0.5555508 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 28.67458 | 86.72278 | 51.74750 | NaN | Inf | 1.7271659 | 0.0313377 |
| ETS(quantity ~ season(“N”)) | Test | -6.13568 | 27.03736 | 21.11563 | -Inf | Inf | 0.7047722 | -0.1100202 |
| prophet(quantity) | Test | 32.13494 | 96.29395 | 52.67246 | NaN | Inf | 1.7580382 | 0.0057382 |
| SNAIVE(quantity) | Test | 10.00000 | 25.81804 | 18.00000 | 50 | 100 | 0.6007824 | 0.1591024 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.124371 |
| ETS(quantity ~ season(method = “N”)) | l | 898.440269 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 15.57969 | 0.112313 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 1.0313879 | 0.0987790 | 10.4413722 | 0.0000000 |
| ARIMA(quantity) | ar2 | -0.0661262 | 0.0897797 | -0.7365376 | 0.4623786 |
| ARIMA(quantity) | ma1 | -0.8414622 | 0.0537101 | -15.6667286 | 0.0000000 |
| ARIMA(quantity) | sar1 | 0.2504092 | 0.0907798 | 2.7584234 | 0.0064183 |
| ARIMA(quantity) | constant | 21.1296806 | 2.2429951 | 9.4202972 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 15.58525 | 0.1121366 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 105.51000 | 263.09 | 222.54 | 4.0375 | 23.232 | 0.90854 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.36505 | 238.05 | 193.23 | -7.4153 | 23.177 | 0.78888 |
| prophet(quantity) | Test | 259.01000 | 350.86 | 313.05 | 20.2220 | 29.580 | 1.27810 |
| SNAIVE(quantity) | Test | 412.42000 | 491.26 | 412.42 | 38.4530 | 38.453 | 1.68370 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 38.529 | 119.500 | 94.770 | -Inf | Inf | 1.14030 |
| ETS(quantity ~ season(method = “N”)) | Test | 11.305 | 140.600 | 112.950 | -Inf | Inf | 1.35900 |
| prophet(quantity) | Test | 26.573 | 77.494 | 54.843 | -Inf | Inf | 0.65987 |
| SNAIVE(quantity) | Test | 60.429 | 111.980 | 77.000 | 26.675 | 61.008 | 0.92646 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 19.277667 | 205.1419 | 133.0653 | -0.5412494 | 15.80380 | 0.5415783 | -0.0745924 |
| ETS(quantity ~ season(method = “N”)) | Test | 26.490351 | 165.8133 | 113.2738 | 0.4867214 | 13.13922 | 0.4610262 | 0.1888127 |
| prophet(quantity) | Test | 377.922408 | 1621.8121 | 836.3426 | 42.6686979 | 118.99848 | 3.4039295 | -0.0866513 |
| SNAIVE(quantity) | Test | 5.833333 | 305.2324 | 226.3333 | -5.2164793 | 26.39360 | 0.9211808 | 0.0746847 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.7452241 | 107.10373 | 87.14089 | -Inf | Inf | 1.0473623 | -0.1114169 |
| ETS(quantity ~ season(“N”)) | Test | 28.1096588 | 161.93995 | 141.41887 | -Inf | Inf | 1.6997392 | -0.2037620 |
| prophet(quantity) | Test | 2.5993510 | 89.46422 | 73.17763 | -Inf | Inf | 0.8795353 | -0.6980208 |
| SNAIVE(quantity) | Test | 43.0000000 | 97.95845 | 69.85714 | 7.329715 | 94.77158 | 0.8396258 | 0.0504905 |
Drug C
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0412606 |
| ETS(quantity ~ season(method = “N”)) | l | 0.2623830 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 17.77709 | 0.0588423 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.0701466 | 0.0586881 | -1.195245 | 0.2328629 |
| ARIMA(quantity) | ma1 | -0.9615223 | 0.0226335 | -42.482203 | 0.0000000 |
| ARIMA(quantity) | constant | 0.0026204 | 0.0018765 | 1.396437 | 0.1635358 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 16.57448 | 0.084326 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.2857800 | 0.46890 | 0.28578 | 19.2700 | 19.270 | 0.39684 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.2930300 | 0.47409 | 0.29303 | 19.9170 | 19.917 | 0.40691 |
| prophet(quantity) | Test | -0.0013524 | 0.40477 | 0.30228 | -7.3543 | 23.009 | 0.41975 |
| SNAIVE(quantity) | Test | 0.3333300 | 0.81650 | 0.66667 | 25.0000 | 58.333 | 0.92573 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.181280 | 0.34152 | 0.18128 | Inf | Inf | 1.3962 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.040362 | 0.29631 | 0.20501 | -Inf | Inf | 1.5790 |
| prophet(quantity) | Test | -0.062591 | 0.28866 | 0.21251 | -Inf | Inf | 1.6367 |
| SNAIVE(quantity) | Test | -0.047619 | 0.43644 | 0.19048 | -Inf | Inf | 1.4671 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0421053 | 0.8393013 | 0.5541804 | -Inf | Inf | 0.7695355 | -0.0275101 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.1150738 | 0.8592692 | 0.6069687 | -Inf | Inf | 0.8428374 | 0.0119434 |
| prophet(quantity) | Test | -0.3007699 | 1.6973211 | 1.0601304 | NaN | Inf | 1.4720982 | -0.0146589 |
| SNAIVE(quantity) | Test | -0.1111111 | 0.9229582 | 0.6296296 | -Inf | Inf | 0.8743044 | 0.0778867 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.1007468 | 0.6269236 | 0.3268215 | NaN | Inf | 2.599233 | 0.0126785 |
| ETS(quantity ~ season(“N”)) | Test | 0.0948670 | 0.5723796 | 0.2320933 | -Inf | Inf | 1.845854 | -0.0568424 |
| prophet(quantity) | Test | 0.1826151 | 0.6488830 | 0.3160797 | NaN | Inf | 2.513803 | -0.0823068 |
| SNAIVE(quantity) | Test | 0.1666667 | 0.5773503 | 0.1666667 | 100 | 100 | 1.325511 | -0.0984848 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0510261 |
| ETS(quantity ~ season(method = “N”)) | l | 0.6459055 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 35.51043 | 0.0001021 |
ARIMA
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 1.1048919 | 0.1516446 | 7.286061 | 0.0000000 |
| ARIMA(quantity) | ar2 | -0.4391590 | 0.1989076 | -2.207855 | 0.0279503 |
| ARIMA(quantity) | ma1 | -1.2172989 | 0.1320716 | -9.216960 | 0.0000000 |
| ARIMA(quantity) | ma2 | 0.6420286 | 0.1789902 | 3.586947 | 0.0003858 |
| ARIMA(quantity) | sar1 | -0.5355094 | NaN | NaN | NaN |
| ARIMA(quantity) | sma1 | 0.5853612 | NaN | NaN | NaN |
| ARIMA(quantity) | constant | 0.3752139 | 0.0369474 | 10.155340 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 23.05706 | 0.0105379 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.049325 | 0.51020 | 0.49213 | -Inf | Inf | 0.49959 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.018531 | 0.47177 | 0.43827 | -Inf | Inf | 0.44491 |
| prophet(quantity) | Test | 0.288300 | 0.56764 | 0.55528 | -Inf | Inf | 0.56369 |
| SNAIVE(quantity) | Test | 0.333330 | 0.81650 | 0.66667 | -Inf | Inf | 0.67677 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.014127 | 0.32413 | 0.19897 | -Inf | Inf | 1.04670 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.022134 | 0.32460 | 0.19289 | -Inf | Inf | 1.01470 |
| prophet(quantity) | Test | 0.039191 | 0.31361 | 0.18020 | NaN | Inf | 0.94797 |
| SNAIVE(quantity) | Test | -0.023810 | 0.51177 | 0.26190 | -Inf | Inf | 1.37780 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.1710114 | 0.9796163 | 0.7320750 | NaN | Inf | 0.7431671 | -0.3364868 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.1108441 | 0.8712828 | 0.7075714 | NaN | Inf | 0.7182922 | -0.3562419 |
| prophet(quantity) | Test | 0.3102135 | 2.6286350 | 1.2303357 | NaN | Inf | 1.2489771 | 0.0609418 |
| SNAIVE(quantity) | Test | -0.4814815 | 1.5515822 | 1.0740741 | -Inf | Inf | 1.0903479 | -0.3664939 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.4303394 | 0.7642420 | 0.4946148 | NaN | Inf | 2.588210 | -0.5597121 |
| ETS(quantity ~ season(“N”)) | Test | 0.3841751 | 0.7525626 | 0.5159125 | -Inf | Inf | 2.699656 | -0.5652191 |
| prophet(quantity) | Test | 0.3750273 | 0.7151440 | 0.4679030 | NaN | Inf | 2.448433 | -0.4655574 |
| SNAIVE(quantity) | Test | 0.4166667 | 0.8660254 | 0.5833333 | -Inf | Inf | 3.052455 | -0.5552209 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0550134 |
| ETS(quantity ~ season(method = “N”)) | l | 4.2467197 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 87.48554 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.9658033 | 0.0347695 | -27.7773420 | 0.0000000 |
| ARIMA(quantity) | ma1 | 0.0096191 | 0.0432232 | 0.2225447 | 0.8240280 |
| ARIMA(quantity) | ma2 | -0.8915537 | 0.0414954 | -21.4855861 | 0.0000000 |
| ARIMA(quantity) | sar1 | -0.1594127 | 0.3129469 | -0.5093921 | 0.6108189 |
| ARIMA(quantity) | sar2 | 0.1753829 | 0.0713690 | 2.4574109 | 0.0145097 |
| ARIMA(quantity) | sma1 | 0.2334420 | 0.3155152 | 0.7398758 | 0.4599030 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 83.66213 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.64151 | 2.4227 | 1.7647 | -Inf | Inf | 0.79338 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.48847 | 2.4071 | 1.7184 | -Inf | Inf | 0.77256 |
| prophet(quantity) | Test | 0.55416 | 2.4603 | 1.9927 | -Inf | Inf | 0.89589 |
| SNAIVE(quantity) | Test | 0.16667 | 3.1885 | 2.8333 | -Inf | Inf | 1.27380 |
Daily data
## Warning in sqrt(diag(best$var.coef)): NaNs produced
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.1059800 | 0.74299 | 0.42298 | -Inf | Inf | 0.67971 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.0486690 | 0.74157 | 0.45893 | -Inf | Inf | 0.73748 |
| prophet(quantity) | Test | -0.0026539 | 0.74186 | 0.48489 | NaN | Inf | 0.77921 |
| SNAIVE(quantity) | Test | 0.0238100 | 0.74001 | 0.40476 | -Inf | Inf | 0.65044 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.4028857 | 2.958575 | 2.081972 | -Inf | Inf | 0.9330576 | -0.0199346 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.2098833 | 2.476379 | 1.896634 | -Inf | Inf | 0.8499965 | -0.2425449 |
| prophet(quantity) | Test | -1.0498828 | 5.379404 | 2.806312 | -Inf | Inf | 1.2576781 | -0.1774882 |
| SNAIVE(quantity) | Test | 0.2592593 | 3.226051 | 2.259259 | -Inf | Inf | 1.0125108 | 0.0461907 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.7978619 | 2.9127925 | 1.3894084 | -Inf | Inf | 2.2084176 | -0.0962338 |
| ETS(quantity ~ season(“N”)) | Test | -0.0928173 | 0.7227666 | 0.6137358 | -Inf | Inf | 0.9755122 | -0.5179068 |
| prophet(quantity) | Test | -0.9396940 | 3.2796915 | 1.3324359 | NaN | Inf | 2.1178616 | -0.0166965 |
| SNAIVE(quantity) | Test | 0.0833333 | 1.1180340 | 0.7500000 | -Inf | Inf | 1.1920996 | -0.6764432 |
Drug D
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.1177532 |
| ETS(quantity ~ season(method = “N”)) | l | 7.9912120 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 35.48464 | 0.0001032 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -0.8780575 | 0.0323965 | -27.1034327 | 0.0000000 |
| ARIMA(quantity) | sar1 | 0.0354841 | 0.0786125 | 0.4513799 | 0.6520441 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 36.34574 | 7.34e-05 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 3.9053 | 11.142 | 5.1743 | -Inf | Inf | 0.49484 |
| ETS(quantity ~ season(method = “N”)) | Test | 3.7817 | 11.099 | 5.2566 | -Inf | Inf | 0.50272 |
| prophet(quantity) | Test | -4.7007 | 10.285 | 9.4090 | -Inf | Inf | 0.89982 |
| SNAIVE(quantity) | Test | 4.6667 | 11.431 | 4.6667 | 100 | 100 | 0.44630 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.63313 | 4.3154 | 0.69861 | -Inf | Inf | 0.42239 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.63792 | 4.3162 | 0.69405 | -Inf | Inf | 0.41963 |
| prophet(quantity) | Test | 0.93829 | 4.4461 | 1.34190 | NaN | Inf | 0.81133 |
| SNAIVE(quantity) | Test | 0.66667 | 4.3205 | 0.66667 | 100 | 100 | 0.40308 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -3.350528 | 18.35454 | 10.628312 | NaN | Inf | 1.0061807 | 0.0928565 |
| ETS(quantity ~ season(method = “N”)) | Test | -2.287967 | 12.84910 | 8.549902 | -Inf | Inf | 0.8094180 | -0.3019281 |
| prophet(quantity) | Test | 17.029606 | 68.01474 | 29.324237 | NaN | Inf | 2.7761211 | 0.4938372 |
| SNAIVE(quantity) | Test | -3.458333 | 19.67337 | 9.625000 | -Inf | Inf | 0.9111973 | 0.3929467 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 1.823933 | 7.611587 | 2.929261 | NaN | Inf | 1.730998 | -0.0458815 |
| ETS(quantity ~ season(“N”)) | Test | 1.429982 | 6.971705 | 2.571545 | -Inf | Inf | 1.519612 | -0.1354480 |
| prophet(quantity) | Test | 2.012822 | 6.207247 | 3.331596 | NaN | Inf | 1.968751 | 0.1677690 |
| SNAIVE(quantity) | Test | 0.000000 | 11.430952 | 4.666667 | -Inf | Inf | 2.757690 | 0.0000000 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0807574 |
| ETS(quantity ~ season(method = “N”)) | l | 17.8629306 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 26.27242 | 0.0033906 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.1995096 | 0.0747021 | -2.670737 | 0.0079493 |
| ARIMA(quantity) | ma1 | -0.8003094 | 0.0616738 | -12.976498 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 16.76456 | 0.0797388 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 11.6770 | 18.153 | 13.893 | -Inf | Inf | 0.43867 |
| ETS(quantity ~ season(method = “N”)) | Test | 7.0046 | 15.509 | 13.833 | -Inf | Inf | 0.43677 |
| prophet(quantity) | Test | 8.1581 | 14.725 | 12.943 | NaN | Inf | 0.40867 |
| SNAIVE(quantity) | Test | 4.5000 | 19.803 | 14.167 | -Inf | Inf | 0.44730 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 1.7259 | 8.3257 | 3.3840 | -Inf | Inf | 0.64965 |
| ETS(quantity ~ season(method = “N”)) | Test | 1.8888 | 8.3638 | 3.2537 | -Inf | Inf | 0.62465 |
| prophet(quantity) | Test | 1.2346 | 8.3503 | 4.4703 | NaN | Inf | 0.85820 |
| SNAIVE(quantity) | Test | 2.6429 | 8.5649 | 2.6429 | 100 | 100 | 0.50737 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -3.486690 | 39.14891 | 25.61079 | -Inf | Inf | 0.8086348 | -0.0057632 |
| ETS(quantity ~ season(method = “N”)) | Test | -3.869129 | 28.28784 | 21.64749 | -Inf | Inf | 0.6834975 | -0.2157579 |
| prophet(quantity) | Test | 13.745053 | 138.73141 | 59.35357 | NaN | Inf | 1.8740287 | -0.0184426 |
| SNAIVE(quantity) | Test | -10.444444 | 41.04018 | 27.03704 | -Inf | Inf | 0.8536671 | -0.1136586 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 16.967734 | 52.97826 | 21.491109 | NaN | Inf | 4.0576717 | -0.0430950 |
| ETS(quantity ~ season(“N”)) | Test | 1.253341 | 11.15908 | 7.142298 | -Inf | Inf | 1.3485159 | -0.0671872 |
| prophet(quantity) | Test | 4.715659 | 22.19332 | 13.641277 | NaN | Inf | 2.5755686 | -0.4438870 |
| SNAIVE(quantity) | Test | 4.666667 | 11.43095 | 4.666667 | 100 | 100 | 0.8810993 | -0.2166667 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0532616 |
| ETS(quantity ~ season(method = “N”)) | l | 107.9514229 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 54.70743 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.8631315 | 0.0787298 | -10.9632122 | 0.0000000 |
| ARIMA(quantity) | ma1 | 0.0236562 | 0.0936657 | 0.2525604 | 0.8007671 |
| ARIMA(quantity) | ma2 | -0.7615099 | 0.0822297 | -9.2607650 | 0.0000000 |
| ARIMA(quantity) | ma3 | -0.1759554 | 0.0590797 | -2.9782710 | 0.0031161 |
| ARIMA(quantity) | sar1 | 0.0159874 | 0.0590524 | 0.2707316 | 0.7867688 |
| ARIMA(quantity) | sar2 | 0.1144626 | 0.0674947 | 1.6958748 | 0.0908643 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 37.74725 | 4.2e-05 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -37.0820 | 39.045 | 37.082 | -Inf | Inf | 0.68225 |
| ETS(quantity ~ season(method = “N”)) | Test | -41.1820 | 42.508 | 41.182 | -Inf | Inf | 0.75768 |
| prophet(quantity) | Test | -6.6428 | 12.662 | 10.402 | NaN | Inf | 0.19137 |
| SNAIVE(quantity) | Test | -28.0000 | 48.497 | 37.333 | -Inf | Inf | 0.68687 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 2.2710 | 9.7607 | 2.2710 | Inf | Inf | 0.17621 |
| ETS(quantity ~ season(method = “N”)) | Test | -3.7615 | 10.1820 | 7.2165 | -Inf | Inf | 0.55992 |
| prophet(quantity) | Test | -1.3711 | 11.4650 | 7.9294 | NaN | Inf | 0.61523 |
| SNAIVE(quantity) | Test | 2.0000 | 9.6609 | 2.0000 | 100 | 100 | 0.15518 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -9.618011 | 55.7533 | 41.92324 | -Inf | Inf | 0.7699190 | -0.3397268 |
| ETS(quantity ~ season(method = “N”)) | Test | -10.791006 | 45.5069 | 36.89630 | -Inf | Inf | 0.6775994 | -0.1251835 |
| prophet(quantity) | Test | 57.231878 | 217.0525 | 95.73090 | -Inf | Inf | 1.7580951 | 0.3462817 |
| SNAIVE(quantity) | Test | -15.444444 | 78.8099 | 57.51852 | -Inf | Inf | 1.0563258 | -0.0885764 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning: Having 3 or more differencing operations is not recommended. Please
## consider reducing the total number of differences.## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced## Warning: Problem with `mutate()` input `ARIMA(quantity)`.
## ℹ NaNs produced
## ℹ Input `ARIMA(quantity)` is `(function (object, ...) ...`.## Warning in sqrt(z[[2L]] * object$sigma2): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -26.213775 | 98.05150 | 42.11526 | NaN | Inf | 3.216833 | 0.0243591 |
| ETS(quantity ~ season(“N”)) | Test | -2.373293 | 20.45453 | 16.39639 | -Inf | Inf | 1.252384 | -0.0963740 |
| prophet(quantity) | Test | -4.913114 | 28.21801 | 21.63406 | NaN | Inf | 1.652446 | 0.0110937 |
| SNAIVE(quantity) | Test | 2.000000 | 21.41650 | 12.00000 | -Inf | Inf | 0.916580 | -0.2969208 |